A boundary element method (BEM) is utilized to find numerical solutions to boundary value problems of homogeneous media governed by as anisotropic-diffusion convection-reaction (DCR) equation. Some problems are considered. A FORTRAN script is developed for the computation of the solutions. The numerical solutions verify the validity of the analysis used to derive the boundary element method with accurate and consistent solutions. The computation shows that the BEM procedure elapses very efficient time in producing the solutions. In addition, results obtained for the considered examples show the effect of the anisotropy of the media on the solutions.

A boundary element method is utilized to find numerical solutions to boundary value problems of exponentially graded media governed by a spatially varying coefficients anisotropic-diffusion convection equation. The variable coefficients equation is firstly transformed into a constant coefficients equation for which a boundary integral equation can be formulated. A boundary element method (BEM) is then derived from the boundary integral equation. Some problems are considered. The numerical solutions justify the validity of the analysis used to derive the boundary element method with accurate and consistent solutions. A FORTRAN script is developed for the computation of the solutions. The computation shows that the BEM procedure elapses very efficient time in producing the solutions. In addition, results obtained from the considered examples show the effect of the anisotropy of the media on the solutions. An example of a layered material is presented as an illustration of the application.

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This paper is concerned with finding numerical solutions to boundary value problems (BVPs) governed by a diffusion convection-reaction (DCR) equation of in-spatial-trigonometrically varying coefficients with an anisotropic diffusion coefficient. The variable coefficients equation is firstly transformed into a constant coefficients equation. A boundary integral equation is the derived from the constant coefficients equation. Consequently, a boundary element method (BEM) is developed and utilized to find numerical solutions to the boundary value problems. For the computation of the solutions for some examples of problems, a FORTRAN script is constructed. The numerical solutions obtained verify the validity of the analysis used to derive the BEM. The results also show that the BEM procedure elapses very efficient time in producing very accurate and consistent solutions. Moreover, the results indicate the effect of anisotropy and inhomogeneity of the media on the solutions.

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The ambiguity function associated with the linear canonical transform (LCT) is a generalization of the one-dimensional ambiguity function using the linear canonical transform, called the linear canonical ambiguity function (LCAF). We first investigate its basic properties such as the complex conjugation, translation and modulation. These properties are extensions of the corresponding versions of the classical ambiguity function. Using the basic relationship between the LCT and LCAF, we derive the inversion and Moyal formulas for the LCAF. Based on a convolution theorem for the LCT, we propose the convolution theorem related to LCAF. Finally, through simulation example, we demonstrate how the proposed convolution generalizes the formulation of the classical ambiguity function convolution.